^{1}, M. Martinelli

^{2}, C. A. Massa

^{2}, L. A Pardi

^{2}and D. Leporini

^{3,a)}

### Abstract

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field electron paramagnetic resonance spectroscopy at two different Larmor frequencies (190 and 285 GHz). Two different regimes separated by a crossover region are evidenced. Below 180 K the rotational times are nearly temperature independent with no apparent distribution. In the temperature range of 180-220 K a large increase of the rotational mobility is observed with the widening of the distribution of correlation times which exhibits two components: (i) a deltalike, temperature-independent component representing the fraction of spin probes which persist in the low-temperature dynamics; (ii) a strongly temperature-dependent component, to be described by a power distribution, representing the fraction of spin probes undergoing activated motion over an exponential distribution of barrier heights . Above 180 K a steep decrease of is evidenced. The shape and the width of do not differ from the reported ones for PS within the errors. For the first time the large increase of the rotational mobility of the spin probe at 180 K is ascribed to the onset of the fast dynamics detected by neutron scattering at .

J. Colmenero and A.P. Sokolov are gratefully acknowledged for helpful discussions.

I. INTRODUCTION

II. EPR BACKGROUND

A. Line shape

B. Model of the rotational motion

C. Adjustable parameters

D. Features of the HF-EPR line shape

III. EXPERIMENTAL DETAILS

IV. RESULTS AND DISCUSSION

A. Low temperature regime:

B. Crossover regime:

C. High temperature regime:

D. Characteristic times of TEMPO in PS

V. CONCLUSIONS

### Key Topics

- Musical analysis
- 52.0
- Rotational correlation time
- 29.0
- Electron paramagnetic resonance spectroscopy
- 16.0
- Rotational dynamics
- 14.0
- Nuclear magnetic resonance
- 6.0

## Figures

Schematic view of the bimodal distribution of correlation times [Eq. (8) with ] for different values of the trapped fraction . , , denotes the shortest correlation time. The delta function is replaced by a narrow Gaussian with a width of 0.01.

Schematic view of the bimodal distribution of correlation times [Eq. (8) with ] for different values of the trapped fraction . , , denotes the shortest correlation time. The delta function is replaced by a narrow Gaussian with a width of 0.01.

Calculated EPR line shapes at 190 GHz of a nitroxide spin probe for different jump angles . SCT model [Eq. (5)]. Top: from the top to the bottom the correlation times are , , , , , , and . Bottom: from the top to the bottom the correlation times are , , , , , , and . The magnetic parameters are , , , , , and . The axis is parallel to the N–O bond, the axis is parallel to the nitrogen and oxygen orbitals containing the unpaired electron, and the axis is perpendicular to the other ones (see Fig. 4 for details). Each curve is convoluted with a Gaussian with a width of 0.15 mT. The vertical lines on the top panel mark the positions of the maxima of the outermost peaks at the slowest relaxation rate. They help the reader to appreciate the shifts of the maxima when the reorientation rate increases.

Calculated EPR line shapes at 190 GHz of a nitroxide spin probe for different jump angles . SCT model [Eq. (5)]. Top: from the top to the bottom the correlation times are , , , , , , and . Bottom: from the top to the bottom the correlation times are , , , , , , and . The magnetic parameters are , , , , , and . The axis is parallel to the N–O bond, the axis is parallel to the nitrogen and oxygen orbitals containing the unpaired electron, and the axis is perpendicular to the other ones (see Fig. 4 for details). Each curve is convoluted with a Gaussian with a width of 0.15 mT. The vertical lines on the top panel mark the positions of the maxima of the outermost peaks at the slowest relaxation rate. They help the reader to appreciate the shifts of the maxima when the reorientation rate increases.

Dependence of the distance between the outermost extrema of the HF-EPR line shape at 190 GHz (see Fig. 2) on the rotational correlation time for small and large jump angles .

Dependence of the distance between the outermost extrema of the HF-EPR line shape at 190 GHz (see Fig. 2) on the rotational correlation time for small and large jump angles .

Chemical structures of PS and the spin probe TEMPO.

Chemical structures of PS and the spin probe TEMPO.

Temperature dependence of the quantity at 190 and 285 GHz of TEMPO in PS (see Fig. 2 for the definition). Continuous line: linear fit with , , . Dashed line: guide for the eye. Inset: average linewidth of the three outermost lines on the right side of the line shape (see Fig. 2).

Temperature dependence of the quantity at 190 and 285 GHz of TEMPO in PS (see Fig. 2 for the definition). Continuous line: linear fit with , , . Dashed line: guide for the eye. Inset: average linewidth of the three outermost lines on the right side of the line shape (see Fig. 2).

The line shape at 190 GHz (a) and 285 GHz (b) of TEMPO in PS at 50 K. The superimposed dashed lines are best fits according to the SCT model, Eq. (5), with (190 GHz) and (285 GHz). Jump angle . Nearly identical agreement is obtained by decreasing the jump angle down to with (190 GHz) and (285 GHz). Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

The line shape at 190 GHz (a) and 285 GHz (b) of TEMPO in PS at 50 K. The superimposed dashed lines are best fits according to the SCT model, Eq. (5), with (190 GHz) and (285 GHz). Jump angle . Nearly identical agreement is obtained by decreasing the jump angle down to with (190 GHz) and (285 GHz). Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

The HF-EPR line shape of TEMPO in PS at 180 K and frequencies 190 GHz (a) and 285 GHz (b). The dotted superimposed lines are simulations by using the SCT model with jump angle and (a); (b). The dashed superimposed line in panel (a) is a simulation using the SCT model with jump angle and . Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

The HF-EPR line shape of TEMPO in PS at 180 K and frequencies 190 GHz (a) and 285 GHz (b). The dotted superimposed lines are simulations by using the SCT model with jump angle and (a); (b). The dashed superimposed line in panel (a) is a simulation using the SCT model with jump angle and . Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

The EPR line shape at and frequencies 190 GHz (a) and 285 GHz (b). The dotted lines are numerical simulations by using the TPD model [Eq. (8) with , Eq. (4)] with , (a); , (b). For each frequency at 180 K and , see Fig. 7. From Eq. (9) the fraction of TEMPO molecules undergoing not activated motion was and . The dashed lines are numerical simulations by using the SCT model with [panel (a)] and [panel (b)]. In both cases the best-fit value of the jump angle is . Notice that the TPD model has only *one* more adjustable parameter with respet to SCT one. Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

The EPR line shape at and frequencies 190 GHz (a) and 285 GHz (b). The dotted lines are numerical simulations by using the TPD model [Eq. (8) with , Eq. (4)] with , (a); , (b). For each frequency at 180 K and , see Fig. 7. From Eq. (9) the fraction of TEMPO molecules undergoing not activated motion was and . The dashed lines are numerical simulations by using the SCT model with [panel (a)] and [panel (b)]. In both cases the best-fit value of the jump angle is . Notice that the TPD model has only *one* more adjustable parameter with respet to SCT one. Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

Temperature dependence of the fraction of trapped TEMPO molecules, Eq. (9).

Temperature dependence of the fraction of trapped TEMPO molecules, Eq. (9).

Best fit of the EPR line shape using SCT, LGD, and PD from 190 GHz, 270 K, and a jump angle . For SCT: ; for LGD: , ; for PD: , . Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

Best fit of the EPR line shape using SCT, LGD, and PD from 190 GHz, 270 K, and a jump angle . For SCT: ; for LGD: , ; for PD: , . Magnetic parameters of TEMPO as in Fig. 2. The theoretical line shape is convoluted by a Gaussian with a width of 0.15 mT to account for the inhomogeneous broadening.

Temperature dependence of the width of the exponential energy-barrier distribution, Eq. (3), as detected by the EPR at 190 GHz (squares) and 285 GHz (triangles). Previous measurements by internal friction (Ref. 31), Raman (Ref. 18), and light scattering (Ref. 28) yield , and , respectively.

Temperature dependence of the width of the exponential energy-barrier distribution, Eq. (3), as detected by the EPR at 190 GHz (squares) and 285 GHz (triangles). Previous measurements by internal friction (Ref. 31), Raman (Ref. 18), and light scattering (Ref. 28) yield , and , respectively.

Temperature dependence of the characteristic times of the SCT, PD, and TPD distributions. The error bars at 50 and 180 K account for the uncertainty on the best-fit value of the jump angle which is in the range of and , respectively. The dotted lines are guides for the eye.

Temperature dependence of the characteristic times of the SCT, PD, and TPD distributions. The error bars at 50 and 180 K account for the uncertainty on the best-fit value of the jump angle which is in the range of and , respectively. The dotted lines are guides for the eye.

The exploration of the orientational energy landscape by TEMPO. : all molecules are trapped (). Orientation correlations are lost via nonactivated entropiclike pathways. : a fraction of the molecules equal to rotate by activated jumps over the exponentially distributed energy barriers.

The exploration of the orientational energy landscape by TEMPO. : all molecules are trapped (). Orientation correlations are lost via nonactivated entropiclike pathways. : a fraction of the molecules equal to rotate by activated jumps over the exponentially distributed energy barriers.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content